Pitch Effect of Helical Coils of Electromagnetic Forming

A Parametric Integral Formulation to Approximate the Magneto Quasi-Static Fields of 3-D Cylindrical Solenoids With Helical Winding

“…and using (17) together with (14), the differential arc length vector's magnitude da ′ may be found, as…”

“…Other works in the literature pertaining to modeling solenoids, include: (i) the work by [17] studies the pitch effect of helical coils, using finite elements software, (ii) the work by [7] proposes a computational model based on the method of finite-difference time-domain (FDTD) for solving the MQS fields of air-core solenoids in 2D space, (iii) the work by [18] develops a field mapping method, based on the scalar magnetic potential, to obtain the z-component of the magnetic field inside air-core solenoids, (iv) the work by [19] proposes an analytical model of the modulated double helical coils, by relying on the infinite thin sheet current approximation, valid for long and tightly-wound windings, and (v) the work by [20] studies the effects of high frequency in sparse-wound solenoids.…”

“…The aforementioned formulations lack in one, or more, of the following ways: (i) they may not be analytical models, instead they rely on computational (finite elements [17] or finite difference [7]) methods that may not offer direct insights into the asymptotic (limiting) effects of geometric and material variables for general solenoids, and their computational nature often implies that conclusions may be confined to the specific solenoid configurations being simulated. Additionally, the simulations are dependent on finite computational resources (memory and processor) and may often experience non-convergence for solenoids of increasing complexity, due to the disparately scaled and quasi-static nature of the problem [7], (ii) they may be two-dimensional approximations of the three-dimensional solenoid and may not include all three orthogonal field components [7], [18], (iii) some analytical models may rely on approximations that are valid only for certain configurations (e.g., infinitely long solenoids [16] and tightly wound windings with an infinitesimal wire pitch [16], [19], circularly symmetric loops [13], certain core material [18], etc.…”

Analytical Model of 3D Helical Solenoids, for Efficient Computation of Dynamic EM Fields, Complex Inductance, and Radiation Resistance

“…Computational models based on spatial discretization (e.g., finite element [11] or finite difference [3]) methods may pose several problems; e.g., (a) they may rely on approximations that are valid only in certain frequency regimes such as quasistatic [12,Maxwell and Q3D] or high frequency [12,HFSS], (b) they may require the inclusion of source and reference (ground) structures that inevitably interfere with characterization of the lone solenoid, (c) they may not offer direct insights into the asymptotic (limiting) effects of geometric and material parameters, (d) their computational nature often implies that conclusions may be confined to the specific solenoid configurations being simulated, (e) they are limited by finite computational resources (memory and processor) and may experience slow-or non-convergence due to disparately multiscaled solenoids [3], and (f) they may be two-dimensional approximations of the three-dimensional solenoid that do not include all three orthogonal field components [3], [10].…”